Friedman-Lemaître-Robertson-Walker

The Friedman-Lemaître-Robertson-Walker (FLRW) metric describes a homogeneousisotropic expanding/contracting universe. Depending on geographical/historical preferences, this may be referred to under the names of a preferred subset of the four scientists Alexander Friedman, Georges Lemaître, Robertson and Walker,
e.g. Friedman-Robertson-Walker (FRW) or Robertson-Walker (RW).

Its metric can be written as

where a(t) is the scale factor of the universe at time t, or or for negative, zero or positive curvature respectively, and , where RC is the (absolute value of the) radius of curvature.

In this formulation of the metric, r gives the comoving distance from the observer, and gives the proper motion distance.

Most cosmologists agree that the observable part of the Universe is well approximated by an almost FLRW model, that is, a model which follows the FLRW metric apart from primordial density fluctuations. In a strictly FLRW model, there are no clusters of galaxies, stars or people, since these are objects much denser than a typical part of the Universe.

However, for brevity, the almost FLRW model is often referred to simply as the FLRW model (or the FRW model).

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